I don't know about Shiny Gold, but there is a hack called Pokemon Liquid Crystal out there that looks great, and I'm not sure, but I think it's finished.
So, I do know that it is possible to run NDS ROMs on the 3DS using compatible flashcarts, but I can't seem to find any information about GBA ROMs compatibility.
I'm sorry if it is a noob question, but is it possible to run GBA ROMs on the 3DS?